In one Canadian lottery option, you bet on one of the million six-digit numbers between 000000 and 999999. For a $1 bet, you win $100,000 if you are correct. In playing n times, let X be the number of times you win.
a. Find the mean of the distribution of X, in terms of n .
b. How large an n is needed for you to expect to win once (that is, np = 1)?
c. If you play the number of times n that you determined in part b, show that your expected winnings is $100,000 but your expected profit is - +900,000.